A time delay bilateral teleoperation control method combining four-channel and time-domain passivity

By combining four-channel and time-domain passive methods, a time-delay energy network and a slave-end equivalent proportional controller are established, solving the stability and transparency issues of the teleoperation system under time-delay conditions, and realizing the safe, stable and transparent perception of the teleoperation system.

CN118707880BActive Publication Date: 2026-02-10ZHEJIANG UNIV
View PDF 2 Cites 0 Cited by

Patent Information

Application Number
CN202410693854.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Priority Date
2024-05-15
Filing Date
2024-05-31
Publication Date
2026-02-10
Estimated Expiration
2044-05-31

AI Technical Summary

Technical Problem

Existing bilateral teleoperation systems struggle to simultaneously guarantee stability and transparency under time-delay conditions, leading to distorted feedback information and system instability.

Method used

A time-delay energy network is established by combining four channels and time-domain passive methods. The force and velocity signals in the communication channel are adjusted by passive observers and passive controllers. The equivalent velocity signal is used to replace the velocity signal in the communication channel, and a slave-end equivalent proportional controller is established to solve the position drift problem.

Benefits of technology

Ensuring the stability and transparency of the remote operating system under time-delay conditions ensures that human operators can perceive the external environment in real time and safely control the robotic arm.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN118707880B_ABST
    Figure CN118707880B_ABST
Patent Text Reader

Abstract

The application discloses a time-delay bilateral teleoperation control method combining four channels and time-domain passivity. The method comprises the following steps: establishing a dynamic model of a bilateral teleoperation system, establishing a time-delay energy network by using a time-domain passivity method, and adjusting force and speed signals; using a four-channel communication channel architecture, inputting the adjusted force and speed signals, operator and external contact environment force into a gain module, and outputting main end and slave end external forces; using an equivalent speed signal to replace a speed signal in the communication channel for transmission; establishing a slave end equivalent proportional controller to solve a position drift problem; establishing main end and slave end feedback passivity controllers to solve a problem that passivity in the time-domain passivity method is irrelevant to the equivalent speed signal, and realizing time-delay bilateral teleoperation control. The method combines the four channels and the time-domain passivity method, and realizes optimal transparency under the condition of ensuring stability of the bilateral teleoperation system.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] This invention relates to a time-delay bilateral teleoperation control method, specifically a time-delay bilateral teleoperation control method combining four channels and time-domain passive control. Background Technology

[0002] With the advancement of industrial technology, especially the development and application of robotics, robots are gradually taking over various repetitive or heavy-duty tasks. However, in some specialized fields, such as space and deep-sea exploration, telemedicine, and nuclear and chemical waste treatment, it remains technically difficult for humans to directly access the work area or for fully autonomous robots to complete tasks independently. Therefore, the method of remotely controlling robots by human operators using a two-sided telecontrol system to achieve exploration and operational goals has become an important solution.

[0003] A bilateral teleoperation system (TBS) consists of a primary human operator, a master force feedback device, a communication channel, a slave robot, and the external contact environment. The human operator locally operates the master force feedback device to issue target commands. These commands are transmitted via the communication channel, and the slave robot receives the commands and moves within the external contact environment. It then feeds back real-time environmental information to the human operator through the communication channel; this ability to reflect the external environment is referred to as transparency. However, actual communication channels often have significant time delays—a time difference between the master robot issuing a command and the slave robot receiving it. This delay can lead to instability in the TBS and even damage to the slave robot. Ensuring the stability of the bilateral TBS under these time delays is a significant challenge.

[0004] The transparency and stability of a bilateral teleoperation system are mutually constrained. Improving system transparency while ensuring system stability remains a problem to be solved in the field of time-delay bilateral teleoperation control. Existing control methods often distort feedback information while ensuring system stability, leading to a decrease in system transparency. Summary of the Invention

[0005] To address the problems existing in the technical background, this invention provides a time-delayed bilateral teleoperation control method combining four channels and time-domain passive technology. This invention uses a time-domain passive method to establish a time-delayed energy network including a passive observer and a passive controller, ensuring the stability of the teleoperation system. Furthermore, it establishes a four-channel communication architecture, transmitting the master and slave position and velocity information separately through communication channels, thereby improving the transparency of the teleoperation system.

[0006] The technical solution adopted in this invention is:

[0007] The present invention provides a time-delayed bilateral teleoperation control method combining four channels and time-domain passive operation, comprising:

[0008] Step 1: Establish a dynamic model of the operator, master force feedback device, slave robot and external contact environment in the bilateral teleoperation system.

[0009] The second step is to establish a time-delay energy network in the communication channel between the master force feedback device and the slave robot using a passive time-domain method based on the dynamic model. The force and velocity signals transmitted by the master force feedback device and the slave robot in the communication channel are adjusted through the time-delay energy network to achieve the stability of the bilateral teleoperation system.

[0010] Step 3: Using a four-channel communication channel architecture, the force and velocity signals of the master force feedback device, adjusted by the time-delay energy network, and the operator's force are input together into the gain module of the four-channel communication channel architecture. After processing, the gain module outputs the external force of the master force feedback device. Similarly, the force and velocity signals of the slave robot, adjusted by the time-delay energy network, and the force from the external contact environment are input together into the gain module of the four-channel communication channel architecture. After processing, the gain module outputs the external force of the slave robot's slave force feedback device. This achieves the transparency of the bilateral teleoperation system and enables the identification of the external forces of the master and slave force feedback devices.

[0011] Step 4: Combine the four-channel communication channel architecture and the time-domain passive method to construct a bilateral teleoperation system. During the signal transmission process of the communication channel, an equivalent velocity signal encoded by both position and velocity information is used to replace the velocity signal in the communication channel for transmission.

[0012] Step 5: Establish a slave-end equivalent proportional controller and master-slave feedback passive controllers under passive constraints; input the equivalent velocity signal into the slave-end equivalent proportional controller, which outputs the slave-end equivalent control force to control the slave robot; input the positions of the master-end force feedback device and the slave robot into the master-slave feedback passive controllers, which output the internal control forces acting on the master-end force feedback device and the slave robot to control them, realizing time-delayed bilateral teleoperation control of the master-end force feedback device and the slave robot. The slave-end equivalent proportional controller solves the position drift problem, and the master-slave feedback passive controllers solve the problem that passivity is independent of the equivalent velocity signal in the time-domain passive method.

[0013] In the first step, the bilateral teleoperation system consists of an operator, a master force feedback device, a slave robot, and an external contact environment. Force and velocity signals from the master force feedback device and the slave robot are transmitted to each other via a communication channel. The specific dynamic models of the operator, master force feedback device, slave robot, and external contact environment in the bilateral teleoperation system are as follows:

[0014] m i ai +b i v i =f i con +f i ext i = m, s

[0015] f j =b j v j +k j x j ,j=h,e

[0016] Where, m i This represents the mass of the master force feedback device or the slave robot. i = m indicates the parameter corresponds to the master force feedback device, and i = s indicates the parameter corresponds to the slave robot. m and m s These represent the masses of the master force feedback device and the slave robot, respectively; a i and v i Let a represent the acceleration and velocity of the master force feedback device or the slave robot, respectively. m and v m Let a represent the acceleration and velocity of the main force feedback device, respectively. s and v s b represents the acceleration and velocity of the slave robot, respectively; i b represents the damping coefficient of the master-end force feedback device or the slave-end robot. m and b s These represent the damping coefficients of the master-end force feedback device and the slave-end robot, respectively; f i con This indicates the internal control force experienced by the master force feedback device or the slave robot. and These represent the internal control forces experienced by the master force feedback device and the slave robot, respectively; f i ext This indicates the external force acting on the master force feedback device or the slave robot. and These represent the external forces acting on the master-end force feedback device and the slave-end robot, respectively, f for the master end and f for the slave end. h and f e ;f j This represents the force exerted by the operator or the external environment, and the corresponding external force f experienced by the master force feedback device or slave robot. i ext Similarly, j = h indicates that the parameter corresponds to the parameter of the human operator, j = e indicates that the parameter corresponds to the parameter of the external contact environment, and f hThis represents the force exerted by the operator, which is the external force acting on the main force feedback device. f e This represents the force exerted by the external contact environment, i.e., the external force experienced by the end-user robot. b j and k j b represents the damping coefficient and elastic coefficient of the operator or the external contact environment, respectively. h and k h b represents the damping coefficient and elastic coefficient of the operator, respectively. e and k e These represent the damping coefficient and elastic coefficient of the external contact environment, respectively; v j and x j These represent the velocity and position of the interaction between the operator and the master force feedback device, or the interaction between the external contact environment and the slave robot, respectively. h and x h These represent the velocity and position of the interaction between the operator and the main force feedback device, respectively. e and x e Let v represent the velocity and position of the interaction between the external contact environment and the slave robot, respectively. In the absence of relative motion, v = ... e =v s ,x e =x s .

[0017] In the second step, the time delay energy network includes a forward time delay energy network and a reverse time delay energy network. The forward time delay energy network includes a forward passive observer and a forward passive controller on both sides of its two ports. The reverse time delay energy network includes a reverse passive observer and a reverse passive controller on both sides of its two ports.

[0018] In a forward time-delay energy network, the velocity v of the master-end force feedback device... m The force f exerted by the external contact environment on the robot is input from one side port. e The external force f input from the other port, adjusted by time delay and the positive passive controller, acts on the slave robot. ed The speed v of the main-end force feedback device, output from one side port and adjusted by the time delay and the positive passive controller, is... md Output from the other port.

[0019] In a reverse time-delay energy network, the force f exerted by the operator on the master-side force feedback device is... h The speed v of the robot is input from one side port. s The speed v of the slave robot, input from the other port and adjusted by the time delay and the reverse passive controller, is... sdThe external force f, output from one port and adjusted by the time delay and reverse passive controller, is received by the main-end force feedback device. hd Output from the other port.

[0020] In the aforementioned forward time-delay energy network, the speed v of the input master-end force feedback device m The force f exerted by the external contact environment on the end-user robot e First, there is a time delay, as detailed below:

[0021]

[0022] in, T represents the speed signal of the master force feedback device after a time delay at time t; f1 (t) represents the forward delay of the energy network from one side to the other at time t; This represents the force signal exerted on the slave robot by the external contact environment after a time delay at time t; T b1 (t) represents the forward delay of the energy network at time t, from one side to the other.

[0023] Then, the second positive passive controller on one side of both ports of the positive time-delay energy network is used to adjust the speed signal of the master-end force feedback device after the time delay. The first positive passive controller on the other side is used to adjust the force signal from the external contact environment experienced by the slave robot after the time delay. Specifically as follows:

[0024]

[0025] Among them, f ed v represents the external force acting on the slave robot after adjustment by the first positive passive controller. md This indicates the speed of the main force feedback device after adjustment by the second positive passive controller; and These represent the control coefficients of the first positive passive controller and the second positive passive controller, respectively. and These represent the energy dissipated by the forward time-delay energy network as observed by the first forward passive observer on one side of the forward time-delay energy network and the energy dissipated by the second forward passive observer on the other side, respectively.

[0026] The energy dissipated by the positive time-delay energy network as observed by the first positive passive observer. And the energy dissipated by the forward time-delay energy network as observed by the second forward passive observer. Specifically as follows:

[0027]

[0028] Where b represents the passivity coefficient, used to connect force and velocity with different dimensions; ∈ represents the time delay coefficient, which represents a conservative estimate of the time-varying time delay with respect to the time derivative.

[0029] and When all are non-negative, the passivity of the positive time-delay energy network can be guaranteed, that is, v is guaranteed. m and f e The passive nature of these two communication channels.

[0030] In the aforementioned reverse time-delay energy network, the input master-end force feedback device is subjected to the force f exerted by the operator. h and the speed v of the end robot s First, there is a time delay, as detailed below:

[0031]

[0032] in, This represents the external force signal received by the master force feedback device after a time delay at time t; T f2 (t) represents the transmission delay of the reverse time-delay energy network from one side to the other at time t; T represents the speed signal of the slave robot after a time delay at time t; b2 (t) represents the transmission delay of the reverse time-delay energy network from one side to the other at time t.

[0033] Then, the first reverse passive controller on one side of the two ports of the reverse time-delay energy network is used to adjust the external force signal received by the master-end force feedback device after the time delay. The second reverse passive controller on the other side is used to adjust the speed signal of the slave robot after the time delay. Specifically as follows:

[0034]

[0035] Among them, v sd f represents the speed of the slave robot after adjustment by the second reverse passive controller. hd This represents the external force acting on the main-end force feedback device after adjustment by the first reverse passive controller; and These represent the control coefficients of the second reverse passive controller and the control coefficients of the first reverse passive controller, respectively. and These represent the energy dissipated by the reverse time-delay energy network as observed by the first reverse passive observer on one side of the reverse time-delay energy network and the energy dissipated by the reverse time-delay energy network as observed by the second reverse passive observer on the other side.

[0036] Due to the time delay, the passivity of the time-delay energy network may not hold. Therefore, a reverse passive controller is established to adjust the transmitted force and velocity signals. and For v sd and f hd The passive controller ensures that the signal adjusted by the passive controller is always non-negative, that is, it ensures v s and f h The passive nature of these two communication channels.

[0037] The energy dissipated by the reverse time-delay energy network is observed by the first reverse passive observer on one side of both ports of the reverse time-delay energy network. And the energy dissipated by the reverse time-delay energy network as observed by the second reverse passive observer on the other side. Specifically as follows:

[0038]

[0039] Where b represents the passivity coefficient; ∈ represents the time delay coefficient.

[0040] and When all values ​​are non-negative, the passivity of the reverse time-delay energy network can be guaranteed, that is, v is guaranteed. s and f h The passive nature of these two communication channels.

[0041] In the third step, for the master force feedback device, the speed v of the master force feedback device is... m The external force f acting on the main force feedback device h The speed v of the slave robot is received after time delay and adjustment by the second reverse passive controller. sd And the external force f acting on the slave robot after time delay and adjustment by the first reverse passive controller. ed Then, with the force f applied by the operator. h In the common input gain module, the output of the gain module processes the external force of the main force feedback device. Specifically as follows:

[0042]

[0043] C2, C4, and C6 represent the second, fourth, and sixth four-channel gain coefficients of the gain module, respectively.

[0044] For the slave robot, the speed v of the slave robot is sent. s and the external force f acting on the end robot e The speed v of the main force feedback device is received after time delay and adjustment by the second positive passive controller. md The external force f acting on the main-end force feedback device after time delay and adjustment by the first positive passive controller hd Then, the force f acting on the external environment. e The inputs are fed into the gain module, which processes the inputs and outputs the external force of the slave force feedback device of the slave robot. Specifically as follows:

[0045]

[0046] Wherein, C1, C3, and C5 represent the first, third, and fifth four-channel gain coefficients of the gain module, respectively; K represents the equivalent control force of the slave robot. pr This represents the equivalent gain coefficient.

[0047] In the fourth step, the equivalent velocity signal is as follows:

[0048] r i =v i +λx i i = m, s

[0049] Where, r i Represents the equivalent velocity signal, r m and r s These represent the speeds v of the main force feedback device. m and the speed v of the end robot s The equivalent velocity signal; λ represents the equivalent velocity coefficient; x i Indicates the position of the master force feedback device or the slave robot, x m and x s These represent the positions of the master force feedback device and the slave robot, respectively.

[0050] In the fifth step, by defining the equivalent velocity signal, position information and velocity information can be encoded together, and a slave-end equivalent proportional controller is established to recover accurate position tracking. The slave-end equivalent proportional controller is as follows:

[0051]

[0052] in, K represents the equivalent control force of the slave robot after adjustment by the slave-end equivalent proportional controller. pr Represents the equivalent gain coefficient; r mdThis represents the speed v of the main-end force feedback device after adjustment by the first positive passive controller. md The equivalent velocity signal, r s The speed v of the slave robot is represented by s The equivalent velocity signal.

[0053] After introducing the equivalent velocity signal, the dynamic model of the master force feedback device and the slave robot, which were originally passive for velocity, no longer have the passive property of the equivalent velocity signal. Therefore, the dynamic model needs to be adjusted to ensure the passivity of the master force feedback device and the slave robot.

[0054] The master and slave feedback passive controllers are as follows:

[0055] f i con =f i FPC i = m, s

[0056]

[0057] Among them, f i con This indicates the internal control force experienced by the master force feedback device or the slave robot. and These represent the internal control forces experienced by the master force feedback device and the slave robot, respectively; f i FPC This indicates the passive control force feedback from the master force feedback device or the slave robot. and f represents the passive control force feedback from the master force feedback device and the slave robot, respectively. i con and The two are equal, meaning the internal control force received by the master-end force feedback device or the slave-end robot is the feedback passive control force; B i and K i B represents the passive damping coefficient and passive gain coefficient of the master force feedback device or the slave robot, respectively. m and K m B represents the passive damping coefficient and passive gain coefficient of the main force feedback device, respectively. s and K s This represents the passive feedback damping coefficient and passive feedback gain coefficient of the slave robot; x i Indicates the position of the master force feedback device or the slave robot, x m and x s These represent the positions of the master force feedback device and the slave robot, respectively. The derivative representing the position of the master force feedback device or the slave robot. and These represent the derivatives of the positions of the master force feedback device and the slave robot, respectively.

[0058] The passive constraint is as follows:

[0059] b i +B i >λm i ,λ>0,K i >0

[0060] Among them, b i b represents the damping coefficient of the master-end force feedback device or the slave-end robot. m and b s Represent the damping coefficients of the master-end force feedback device and the slave-end robot, respectively; λ represents the equivalent velocity coefficient; m i Indicates the mass of the master force feedback device or the slave robot, m m and m s These represent the mass of the master force feedback device and the slave robot, respectively.

[0061] The beneficial effects of this invention are:

[0062] 1. This invention uses a time-domain passive method to establish a time-delay energy network including a passive observer and a passive controller, which ensures the stability of the teleoperation system under the condition of time-varying delay in the communication channel and ensures the safety of human operators when operating the robotic arm.

[0063] 2. This invention establishes a four-channel communication architecture, which transmits the position and speed information of the master and slave ends through communication channels respectively, thereby improving the transparency of the remote operating system and facilitating human operators to perceive the external contact environment in real time and react accordingly. Attached Figure Description

[0064] Figure 1 This is a system diagram of the method of the present invention;

[0065] Figure 2 These are internal structural diagrams of the forward and reverse time-delay energy networks of this invention;

[0066] Figure 3 This is a schematic diagram of the slave-end equivalent proportional controller and the feedback passive controller of the present invention;

[0067] Figure 4 This is an experimental diagram showing the position and force tracking results of the teleoperation system of the present invention. Figure 4 (a) is an experimental result diagram of the remote operating system position signal tracking of the present invention. Figure 4 (b) is an experimental result diagram of the remote operating system force signal tracking of the present invention;

[0068] Figure 5This is a schematic diagram illustrating the stability of the teleoperation system of the present invention, wherein, Figure 5 (a) is a schematic diagram of the dissipated energy observed by the passive observer before and after the adjustment of the passive controller on the left side of the teleoperation system of the present invention. Figure 5 (b) is a schematic diagram of the dissipated energy observed by the passive observer before and after the adjustment of the passive controller on the right side of the remote operating system of the present invention. Figure 5 (c) is a schematic diagram of the dissipated energy observed by the passive observer before and after the adjustment of the passive controller on the reverse left side of the teleoperation system of the present invention. Figure 5 (d) is a schematic diagram of the dissipated energy observed by the passive observer before and after the adjustment of the passive controller on the reverse right side of the remote operating system of the present invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0070] The time-delayed bilateral teleoperation control method combining four channels and time-domain passive technology of the present invention is as follows:

[0071] Step 1: Establish a dynamic model of the operator, master force feedback device, slave robot and external contact environment in the bilateral teleoperation system.

[0072] In the first step, the bilateral teleoperation system consists of an operator, a master force feedback device, a slave robot, and an external contact environment. Force and velocity signals from the master force feedback device and the slave robot are transmitted to each other via a communication channel. The specific dynamic models of the operator, master force feedback device, slave robot, and external contact environment in the bilateral teleoperation system are as follows:

[0073] m i a i +b i v i =f i con +f i ext i = m, s

[0074] f j =b j v j +k j x j ,j=h,e

[0075] Where, m iThis represents the mass of the master force feedback device or the slave robot. i = m indicates the parameter corresponds to the master force feedback device, and i = s indicates the parameter corresponds to the slave robot. m and m s These represent the masses of the master force feedback device and the slave robot, respectively; a i and v i Let a represent the acceleration and velocity of the master force feedback device or the slave robot, respectively. m and v m Let a represent the acceleration and velocity of the main force feedback device, respectively. s and v s b represents the acceleration and velocity of the slave robot, respectively; i b represents the damping coefficient of the master-end force feedback device or the slave-end robot. m and b s These represent the damping coefficients of the master-end force feedback device and the slave-end robot, respectively; f i con This indicates the internal control force experienced by the master force feedback device or the slave robot. and These represent the internal control forces experienced by the master force feedback device and the slave robot, respectively; f i ext This indicates the external force acting on the master force feedback device or the slave robot. and These represent the external forces acting on the master-end force feedback device and the slave-end robot, respectively, f for the master end and f for the slave end. h and f e ;f j This represents the force exerted by the operator or the external environment, and the corresponding external force f experienced by the master force feedback device or slave robot. i ext Similarly, j = h indicates that the parameter corresponds to the parameter of the human operator, j = e indicates that the parameter corresponds to the parameter of the external contact environment, and f h This represents the force exerted by the operator, which is the external force acting on the main force feedback device. f e This represents the force exerted by the external contact environment, i.e., the external force experienced by the end-user robot. b j and k j b represents the damping coefficient and elastic coefficient of the operator or the external contact environment, respectively. h and k h b represents the damping coefficient and elastic coefficient of the operator, respectively. e and k e These represent the damping coefficient and elastic coefficient of the external contact environment, respectively; v j and xj These represent the velocity and position of the interaction between the operator and the master force feedback device, or the interaction between the external contact environment and the slave robot, respectively. h and x h These represent the velocity and position of the interaction between the operator and the main force feedback device, respectively. e and x e Let v represent the velocity and position of the interaction between the external contact environment and the slave robot, respectively. In the absence of relative motion, v = ... e =v s ,x e =x s .

[0076] The signal transmitted from the master force feedback device to the slave robot via the communication channel is the speed v of the master force feedback device. m The external force f acting on the main force feedback device h The signal transmitted from the slave robot to the master force feedback device through the communication channel is the velocity v of the slave robot. s and the external force f acting on the end robot e .

[0077] The second step is to establish a time-delay energy network in the communication channel between the master force feedback device and the slave robot using a passive time-domain method based on the dynamic model. The force and velocity signals transmitted by the master force feedback device and the slave robot in the communication channel are adjusted through the time-delay energy network to achieve the stability of the bilateral teleoperation system.

[0078] In the second step, the time delay energy network includes a forward time delay energy network and a reverse time delay energy network. The forward time delay energy network includes a forward passive observer and a forward passive controller on both sides of its two ports. The reverse time delay energy network includes a reverse passive observer and a reverse passive controller on both sides of its two ports.

[0079] In a forward time-delay energy network, the velocity v of the master-end force feedback device... m The force f exerted by the external contact environment on the robot is input from one side port. e The external force f input from the other port, adjusted by time delay and the positive passive controller, acts on the slave robot. ed The speed v of the main-end force feedback device, output from one side port and adjusted by the time delay and the positive passive controller, is... md Output from the other port.

[0080] In a reverse time-delay energy network, the force f exerted by the operator on the master-side force feedback device is... h The speed v of the robot is input from one side port. sThe speed v of the slave robot, input from the other port and adjusted by the time delay and the reverse passive controller, is... sd The external force f, output from one port and adjusted by the time delay and reverse passive controller, is received by the main-end force feedback device. hd Output from the other port.

[0081] The established forward and reverse time-delay energy networks can guarantee the passivity of the communication channels for the four transmitted force and velocity signals, i.e., the passivity of the entire communication channel. In a bilateral teleoperation system, the human operator, the master-end force feedback device, the slave-end robot, and the external contact environment can all be considered passive. Therefore, ensuring the passivity of the communication channels establishes the passivity of the bilateral teleoperation system and achieves its stability.

[0082] In a forward time-delay energy network, the speed v of the input master-end force feedback device m The force f exerted by the external contact environment on the end-user robot e First, there is a time delay, as detailed below:

[0083]

[0084] in, T represents the speed signal of the master force feedback device after a time delay at time t; f1 (t) represents the forward delay of the energy network from one side to the other at time t; This represents the force signal exerted on the slave robot by the external contact environment after a time delay at time t; T b1 (t) represents the forward delay of the energy network at time t, from one side to the other.

[0085] Then, the second positive passive controller on one side of both ports of the positive time-delay energy network is used to adjust the speed signal of the master-end force feedback device after the time delay. The first positive passive controller on the other side is used to adjust the force signal from the external contact environment experienced by the slave robot after the time delay. Specifically as follows:

[0086]

[0087] Among them, f ed v represents the external force acting on the slave robot after adjustment by the first positive passive controller. md This indicates the speed of the main force feedback device after adjustment by the second positive passive controller; and These represent the control coefficients of the first positive passive controller and the second positive passive controller, respectively. and These represent the energy dissipated by the forward time-delay energy network as observed by the first forward passive observer on one side of the forward time-delay energy network and the energy dissipated by the second forward passive observer on the other side, respectively.

[0088] Due to the time delay, the passivity of the time-delay energy network may not hold. Therefore, a positive passive controller is established to adjust the transmitted force and velocity signals. and f ed and v md The passive controller ensures that the signal adjusted by the passive controller is always non-negative, that is, it ensures f e and v m The passive nature of these two communication channels.

[0089] The energy dissipated by the forward time-delay energy network as observed by the first forward passive observer. And the energy dissipated by the forward time-delay energy network as observed by the second forward passive observer. Specifically as follows:

[0090]

[0091] Where b represents the passivity coefficient, used to connect force and velocity with different dimensions; ∈ represents the time delay coefficient, which represents a conservative estimate of the time-varying time delay with respect to the time derivative.

[0092] and When all are non-negative, the passivity of the positive time-delay energy network can be guaranteed, that is, v is guaranteed. m and f e The passive nature of these two communication channels.

[0093] In a reverse time-delay energy network, the input master-end force feedback device experiences the force f exerted by the operator. h and the speed v of the end robot s First, there is a time delay, as detailed below:

[0094]

[0095] in, This represents the external force signal received by the master force feedback device after a time delay at time t; T f2 (t) represents the transmission delay of the reverse time-delay energy network from one side to the other at time t; T represents the speed signal of the slave robot after a time delay at time t; b2 (t) represents the transmission delay of the reverse time-delay energy network from one side to the other at time t.

[0096] Then, the first reverse passive controller on one side of the two ports of the reverse time-delay energy network is used to adjust the external force signal received by the master-end force feedback device after the time delay. The second reverse passive controller on the other side is used to adjust the speed signal of the slave robot after the time delay. Specifically as follows:

[0097]

[0098] Among them, v sd f represents the speed of the slave robot after adjustment by the second reverse passive controller. hd This represents the external force acting on the main-end force feedback device after adjustment by the first reverse passive controller; and These represent the control coefficients of the second reverse passive controller and the control coefficients of the first reverse passive controller, respectively. and These represent the energy dissipated by the reverse time-delay energy network as observed by the first reverse passive observer on one side of the reverse time-delay energy network and the energy dissipated by the reverse time-delay energy network as observed by the second reverse passive observer on the other side.

[0099] Due to the time delay, the passivity of the time-delay energy network may not hold. Therefore, a reverse passive controller is established to adjust the transmitted force and velocity signals. and For v sd and f hd The passive controller ensures that the signal adjusted by the passive controller is always non-negative, that is, it ensures v s and f h The passive nature of these two communication channels.

[0100] The energy dissipated by the reverse time-delay energy network as observed by the first reverse passive observer on one side of the two ports of the reverse time-delay energy network. And the energy dissipated by the reverse time-delay energy network as observed by the second reverse passive observer on the other side. Specifically as follows:

[0101]

[0102] Where b represents the passivity coefficient; ∈ represents the time delay coefficient.

[0103] and When all values ​​are non-negative, the passivity of the reverse time-delay energy network can be guaranteed, that is, v is guaranteed. s and f h The passive nature of these two communication channels.

[0104] Step 3: Using a four-channel communication channel architecture, the force and velocity signals of the master force feedback device, adjusted by the time-delay energy network, and the operator's force are input into the gain module of the four-channel communication channel architecture. After processing, the gain module outputs the external force of the master force feedback device. Similarly, the force and velocity signals of the slave robot, adjusted by the time-delay energy network, and the force from the external contact environment are input into the gain module of the four-channel communication channel architecture. After processing, the gain module outputs the external force of the slave robot's slave force feedback device. This achieves the transparency of the bilateral teleoperation system and enables the identification of the external forces of the master and slave force feedback devices.

[0105] In the third step, for the master force feedback device, the speed v of the master force feedback device is sent. m The external force f acting on the main force feedback device h The speed v of the slave robot is received after time delay and adjustment by the second reverse passive controller. sd And the external force f acting on the slave robot after time delay and adjustment by the first reverse passive controller. ed Then, with the force f applied by the operator. h In the common input gain module, the output of the gain module processes the external force of the main force feedback device. Specifically as follows:

[0106]

[0107] C2, C4, and C6 represent the second, fourth, and sixth four-channel gain coefficients of the gain module, respectively.

[0108] For the slave robot, the speed v of the slave robot is sent. s and the external force f acting on the end robot e The speed v of the main force feedback device is received after time delay and adjustment by the second positive passive controller. md The external force f acting on the main-end force feedback device after time delay and adjustment by the first positive passive controller hd Then, the force f acting on the external environment. e The inputs are fed into the gain module, which processes the inputs and outputs the external force of the slave force feedback device of the slave robot. Specifically as follows:

[0109]

[0110] Wherein, C1, C3, and C5 represent the first, third, and fifth four-channel gain coefficients of the gain module, respectively; K represents the equivalent control force of the slave robot. pr This represents the equivalent gain coefficient.

[0111] Step 4: Combine the four-channel communication channel architecture and the time-domain passive method to construct a bilateral teleoperation system. During the signal transmission process of the communication channel, an equivalent velocity signal encoded by both position and velocity information is used to replace the velocity signal in the communication channel for transmission.

[0112] In the fourth step, the equivalent velocity signal is as follows:

[0113] r i =v i +λx i i = m, s

[0114] Where, r i Represents the equivalent velocity signal, r m and r s These represent the speeds v of the main force feedback device. m and the speed v of the end robot s The equivalent velocity signal; λ represents the equivalent velocity coefficient; x i Indicates the position of the master force feedback device or the slave robot, x m and x s These represent the positions of the master force feedback device and the slave robot, respectively.

[0115] Because the signal transmitted through the communication channel is the velocity v of the master force feedback device. m and the speed v of the end robot s However, the actual information reflecting the positions of the master-end force feedback device and the slave-end robot can only be indirectly obtained by integrating the velocity information, which leads to position drift. To solve the position drift problem, an equivalent velocity signal r encoded by both position and velocity information is used. m and r s Speed ​​signal v in alternative communication channel m and v s Transmit the data.

[0116] Step 5: Establish a slave-end equivalent proportional controller and master-slave feedback passive controllers under passive constraints; input the equivalent velocity signal into the slave-end equivalent proportional controller, which outputs the slave-end equivalent control force to control the slave robot; input the positions of the master-end force feedback device and the slave robot into the master-slave feedback passive controllers, which output the internal control forces acting on the master-end force feedback device and the slave robot to control them, realizing time-delayed bilateral teleoperation control of the master-end force feedback device and the slave robot. The slave-end equivalent proportional controller solves the position drift problem, and the master-slave feedback passive controllers solve the problem that passivity is independent of the equivalent velocity signal in the time-domain passive method.

[0117] In the fifth step, by defining the equivalent velocity signal, position information and velocity information can be encoded together, and a slave-end equivalent proportional controller is established to recover accurate position tracking. The slave-end equivalent proportional controller is as follows:

[0118]

[0119] in, K represents the equivalent control force of the slave robot after adjustment by the slave-end equivalent proportional controller. pr Represents the equivalent gain coefficient; r md This represents the speed v of the main-end force feedback device after adjustment by the first positive passive controller. md The equivalent velocity signal, r s The speed v of the slave robot is represented by s The equivalent velocity signal.

[0120] The slave-side equivalent proportional controller is similar to a position error PD controller. Under the action of this controller, the position information does not need to be obtained by integrating the velocity information. Therefore, the slave end can obtain an accurate and unmodified position command, thus solving the position drift problem.

[0121] After introducing the equivalent velocity signal, the dynamic model of the master force feedback device and the slave robot, which were originally passive for velocity, no longer have the passive property of the equivalent velocity signal. Therefore, the dynamic model needs to be adjusted to ensure the passivity of the master force feedback device and the slave robot.

[0122] The master and slave feedback passive controllers are as follows:

[0123] f i con =f i FPC i = m, s

[0124]

[0125] Among them, f i con This indicates the internal control force experienced by the master force feedback device or the slave robot. and These represent the internal control forces experienced by the master force feedback device and the slave robot, respectively; f i FPC This indicates the passive control force feedback from the master force feedback device or the slave robot. and f represents the passive control force feedback from the master force feedback device and the slave robot, respectively. i con and The two are equal, meaning the internal control force received by the master-end force feedback device or the slave-end robot is the feedback passive control force; B i and K i B represents the passive damping coefficient and passive gain coefficient of the master force feedback device or the slave robot, respectively. m and K m B represents the passive damping coefficient and passive gain coefficient of the main force feedback device, respectively. s and K s This represents the passive feedback damping coefficient and passive feedback gain coefficient of the slave robot; x i Indicates the position of the master force feedback device or the slave robot, x m and x s These represent the positions of the master force feedback device and the slave robot, respectively. The derivative representing the position of the master force feedback device or the slave robot. and These represent the derivatives of the positions of the master force feedback device and the slave robot, respectively.

[0126] The passive constraint is as follows:

[0127] b i +B i >λm i ,λ>0,K i >0

[0128] Among them, b i b represents the damping coefficient of the master-end force feedback device or the slave-end robot. m and b s Represent the damping coefficients of the master-end force feedback device and the slave-end robot, respectively; λ represents the equivalent velocity coefficient; m i Indicates the mass of the master force feedback device or the slave robot, m m and m s These represent the mass of the master force feedback device and the slave robot, respectively.

[0129] like Figure 1 As shown, the bilateral teleoperation system mainly consists of a human operator, a master force feedback device, a communication channel, a slave robot, and the external contact environment. The human operator applies force f... h The force feedback device at the main end issues a command, force signal f h and equivalent velocity signal r m Transmission is sent to the slave robot via two of the four communication channels. To ensure the system's passivity, forward and reverse time-delay energy networks are established within the communication channels, with the following structure: Figure 2As shown, the transmitted force and equivalent velocity signals are adjusted by a passive observer and a passive controller. After adjustment, the signals are received by the slave robot through a four-channel gain module, and the slave robot moves to the target position according to the command. The slave robot simultaneously receives the force f from the external contact environment. e , force signal f e and equivalent velocity signal r s The force feedback signal is transmitted to the master-end force feedback device via two additional communication channels out of the four channels. The forward and reverse time-delay energy networks established in these channels, through passive observers and passive controllers, adjust the transmitted force and equivalent velocity signals to ensure the system's passivity. After adjustment, the signal passes through the four-channel gain module and is received by the master-end robot. The master-end robot reflects the forces acting on it from the external environment, which are then perceived and reacted upon by the human operator.

[0130] like Figure 3 As shown, two other important controllers in a time-delayed bilateral teleoperation system combining four channels and time-domain passive characteristics are presented. Based on the equivalent velocity signal, an equivalent proportional controller C is established at the slave end. s The equivalent velocity signal r transmitted from the master end, after passing through the time-delay energy network and four-channel gain, md Equivalent velocity signal r from the slave end s After subtraction, and then equivalent gain, the adjusted slave-end equivalent control force is obtained. This addresses the position drift problem inherent in typical passive time-domain methods. Since the equivalent velocity signal cannot directly establish a passive relationship with the master force feedback device and the slave robot, a master-slave feedback passive controller is used to modify the original dynamic models of the master force feedback device and the slave robot, enabling them to obtain the required equivalent velocity signal using the force signal while maintaining passivity.

[0131] Specific embodiments of the present invention are as follows:

[0132] The effectiveness of the proposed invention, combining a four-channel and time-domain passive time-delay bilateral teleoperation control method, was verified through experiments on the Simulink platform. For the four-channel gain coefficients, C1 = 0.4, C2 = 1, C3 = 1, C4 = 0.4, C5 = 0, and C6 = 0 were chosen to achieve optimal transparency. To make the data more intuitive, a single-degree-of-freedom slave robot was considered in the experimental modeling, and the parameters are shown in Table 1.

[0133] Table 1. Parameter values ​​for the experimental model

[0134]

[0135] During the experiment, the force f applied by the human operator h Given the human operator position x, which varies sinusoidally mObtained through a human operator model. For example... Figure 4 (a) and Figure 4 As shown in (b), the experimental results of the teleoperation system's position and force tracking are presented, demonstrating that under the four-channel and time-domain passive time-delay bilateral teleoperation control method, the system achieves good operational performance and exhibits good transparency. Figure 5 of (a), Figure 5 (b) Figure 5 (c) and Figure 5 As shown in (d), the energy dissipation values ​​of the system communication channel before and after adjustment by the passive controller are observed by the passive observer in the forward and reverse time-delay energy networks. The adjusted dissipation energy value is always non-negative, which shows that the four-channel and time-domain passive time-delay bilateral teleoperation control method ensures the stability of the teleoperation system.

[0136] This invention combines a four-channel and time-domain passive time-delay bilateral teleoperation control method. On one hand, it uses a time-domain passive method to establish a time-delay energy network including a passive observer and a passive controller, ensuring the stability of the teleoperation system under time-varying delay conditions in the communication channel and ensuring the safety of human operators when manipulating the robotic arm. On the other hand, it establishes a four-channel communication architecture, transmitting the master and slave position and speed information separately through the communication channel, improving the transparency of the teleoperation system and facilitating real-time perception and response by the human operator to the external environment.

[0137] The above content is merely a technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A time-delayed bilateral teleoperation control method combining four channels and time-domain passive operation, characterized in that, include: Step 1: Establish a dynamic model of the operator, master force feedback device, slave robot, and external contact environment in the bilateral teleoperation system; Step 2: Based on the dynamic model, using the passive time-domain method, establish a time-delay energy network in the communication channel between the master force feedback device and the slave robot, and adjust the force and velocity signals transmitted by the master force feedback device and the slave robot in the communication channel through the time-delay energy network; Step 3: Using a four-channel communication channel architecture, the force and velocity signals of the master force feedback device, adjusted by the time-delay energy network, and the operator's force are input into the gain module of the four-channel communication channel architecture. After processing, the gain module outputs the external force of the master force feedback device. Similarly, the force and velocity signals of the slave robot, adjusted by the time-delay energy network, and the force from the external contact environment are input into the gain module of the four-channel communication channel architecture. After processing, the gain module outputs the external force of the slave robot's slave force feedback device, thus realizing the identification of the external forces of the master and slave force feedback devices. Step 4: During signal transmission in the communication channel, an equivalent velocity signal is used to replace the velocity signal in the communication channel for transmission; Step 5: Establish a slave-end equivalent proportional controller and master-slave feedback passive controllers under passive constraints; input the equivalent speed signal into the slave-end equivalent proportional controller, and the slave-end equivalent proportional controller outputs the slave-end equivalent control force to control the slave robot; input the positions of the master-end force feedback device and the slave robot into the master-slave feedback passive controllers, and the master-slave feedback passive controllers output the internal control force received by the master-end force feedback device and the slave robot to control the master-end force feedback device and the slave robot, thereby realizing time-delayed bilateral teleoperation control of the master-end force feedback device and the slave robot; In the second step, the time delay energy network includes a forward time delay energy network and a reverse time delay energy network. The forward time delay energy network includes a forward passive observer and a forward passive controller on both sides of its two ports. The reverse time delay energy network includes a reverse passive observer and a reverse passive controller on both sides of its two ports. In the aforementioned forward time-delay energy network, the speed of the input master-end force feedback device and the forces exerted on the end-user robot by the external contact environment First, there is a time delay, as detailed below: ; in, This represents the speed signal of the main force feedback device after a time delay at time t; This represents the forward delay of the energy network from one side to the other at time t. This represents the force signal exerted on the slave robot by the external contact environment after a time delay at time t; This represents the forward delay of the energy network at time t, from one side to the other. Then, the second positive passive controller on one side of both ports of the positive time-delay energy network is used to adjust the speed signal of the master-end force feedback device after the time delay. The first positive passive controller on the other side is used to adjust the force signal from the external contact environment experienced by the slave robot after the time delay. The details are as follows: ; in, This represents the external force acting on the slave robot after adjustment by the first positive passive controller. This indicates the speed of the main force feedback device after adjustment by the second positive passive controller; and These represent the control coefficients of the first positive passive controller and the second positive passive controller, respectively. and These represent the energy dissipated by the forward time-delay energy network as observed by the first forward passive observer on one side of the forward time-delay energy network and the energy dissipated by the forward time-delay energy network as observed by the second forward passive observer on the other side, respectively. In the aforementioned reverse time-delay energy network, the input master-end force feedback device is subjected to the force exerted by the operator. and the speed of the end robot First, there is a time delay, as detailed below: ; in, This represents the external force signal received by the master force feedback device after a time delay at time t; This represents the transmission delay of the reverse-delay energy network from one side to the other at time t; This represents the speed signal of the slave robot after a time delay at time t; This represents the transmission delay of the reverse-delay energy network from one side to the other at time t. Then, the first reverse passive controller on one side of the two ports of the reverse time-delay energy network is used to adjust the external force signal received by the master-end force feedback device after the time delay. The second reverse passive controller on the other side is used to adjust the time-delayed speed signal of the slave robot. The details are as follows: ; in, This indicates the speed of the slave robot after adjustment by the second reverse passive controller. This represents the external force acting on the main-end force feedback device after adjustment by the first reverse passive controller; and These represent the control coefficients of the second reverse passive controller and the control coefficients of the first reverse passive controller, respectively. and These represent the energy dissipated by the reverse time delay energy network as observed by the first reverse passive observer on one side of the reverse time delay energy network and the energy dissipated by the reverse time delay energy network as observed by the second reverse passive observer on the other side, respectively. In the third step, for the master force feedback device, the speed of the master force feedback device is... External forces acting on the main force feedback device Receives the speed of the slave robot after time delay and adjustment by the second reverse passive controller. And the external forces acting on the slave robot after time delay and adjustment by the first reverse passive controller. Then, with the force exerted by the operator In the common input gain module, the output of the gain module processes the external force of the main force feedback device. The details are as follows: ; in, , and These represent the second, fourth, and sixth four-channel gain coefficients of the gain module, respectively. For the slave robot, the speed at which the slave robot sends the data... and the external forces acting on the end robot The speed of the main force feedback device is received after time delay and adjustment by the second positive passive controller. The external force experienced by the main-end force feedback device after time delay and adjustment by the first positive passive controller Then, the forces acting on the external environment. The inputs are fed into the gain module, which processes the inputs and outputs the external force of the slave force feedback device of the slave robot. The details are as follows: ; ; in, , and These represent the first, third, and fifth four-channel gain coefficients of the gain module, respectively. This represents the equivalent control force of the slave robot. This represents the equivalent gain coefficient.

2. The time-delay bilateral teleoperation control method combining four channels and time-domain passive operation as described in claim 1, characterized in that: In the first step, the bilateral teleoperation system consists of an operator, a master force feedback device, a slave robot, and an external contact environment. Force and velocity signals from the master force feedback device and the slave robot are transmitted to each other via a communication channel. The specific dynamic models of the operator, master force feedback device, slave robot, and external contact environment in the bilateral teleoperation system are as follows: ; ; in, This indicates the mass of the master force feedback device or the slave robot. and These represent the masses of the master force feedback device and the slave robot, respectively. and These represent the acceleration and velocity of the master force feedback device or the slave robot, respectively. and These represent the acceleration and velocity of the main force feedback device, respectively. and These represent the acceleration and velocity of the slave robot, respectively. This represents the damping coefficient of the master-end force feedback device or the slave-end robot. and These represent the damping coefficients of the master-end force feedback device and the slave-end robot, respectively. This indicates the internal control force experienced by the master force feedback device or the slave robot. and These represent the internal control forces experienced by the master force feedback device and the slave robot, respectively. This indicates the external force acting on the master force feedback device or the slave robot. and These represent the external forces acting on the master force feedback device and the slave robot, respectively. This indicates the force exerted by the operator or the external environment. This represents the force exerted by the operator, which is the external force acting on the main force feedback device. , This represents the force exerted by the external contact environment, i.e., the external force experienced by the end-user robot. ; and These represent the damping coefficient and elastic coefficient of the operator or the external contact environment, respectively. and These represent the damping coefficient and elastic coefficient of the operator, respectively. and These represent the damping coefficient and elastic coefficient of the external contact environment, respectively; and These represent the speed and position of the interaction between the operator and the master force feedback device, or the interaction between the external contact environment and the slave robot, respectively. and These represent the speed and position of the interaction between the operator and the main force feedback device, respectively. and These represent the speed and position of the interaction between the external contact environment and the slave robot, respectively.

3. The time-delay bilateral teleoperation control method combining four channels and time-domain passive operation as described in claim 1, characterized in that: In the second step, in the forward time-delay energy network, the speed of the master-end force feedback device... The force exerted on the robot by the external contact environment is input from one side port. The external force received from the other port, adjusted by a time delay and a positive passive controller, affects the slave robot. The speed of the main-end force feedback device output from one side port, after time delay and adjustment by the positive passive controller. Output from the other port; In a reverse time-delay energy network, the force exerted by the operator on the master-side force feedback device is... Input from one side port: speed of the slave robot The speed of the slave robot, input from the other port and adjusted by a time delay and a reverse passive controller, is... The external force received by the main-end force feedback device, after being output from one side port and adjusted by a time delay and a reverse passive controller, is... Output from the other port.

4. The time-delay bilateral teleoperation control method combining four channels and time-domain passive operation as described in claim 1, characterized in that: The energy dissipated by the positive time-delay energy network as observed by the first positive passive observer. And the energy dissipated by the forward time-delay energy network as observed by the second forward passive observer. Specifically as follows: ; in, Represents the passivity coefficient; This represents the time delay coefficient.

5. The time-delay bilateral teleoperation control method combining four channels and time-domain passive operation as described in claim 1, characterized in that: The energy dissipated by the reverse time-delay energy network is observed by the first reverse passive observer on one side of both ports of the reverse time-delay energy network. And the energy dissipated by the reverse time-delay energy network as observed by the second reverse passive observer on the other side. Specifically as follows: ; in, Represents the passivity coefficient; This represents the time delay coefficient.

6. The time-delay bilateral teleoperation control method combining four channels and time-domain passive operation as described in claim 1, characterized in that: In the fourth step, the equivalent velocity signal is as follows: ; in, Represents the equivalent velocity signal. and These represent the speeds of the main force feedback device. and the speed of the end robot The equivalent velocity signal; Indicates the equivalent velocity coefficient; Indicates the position of the master force feedback device or the slave robot. and These represent the positions of the master force feedback device and the slave robot, respectively.

7. The time-delay bilateral teleoperation control method combining four channels and time-domain passive operation as described in claim 1, characterized in that: In the fifth step, the slave-side equivalent proportional controller is specifically as follows: ; in, This represents the equivalent control force of the slave robot after adjustment by the slave-end equivalent proportional controller; Represents the equivalent gain coefficient; This indicates the speed of the main-end force feedback device after adjustment by the first positive passive controller. The equivalent velocity signal, Indicates the speed of the slave robot The equivalent velocity signal; The master and slave feedback passive controllers are as follows: ; ; in, This indicates the internal control force experienced by the master force feedback device or the slave robot. and These represent the internal control forces experienced by the master force feedback device and the slave robot, respectively. This indicates the passive control force feedback from the master-end force feedback device or the slave-end robot. and These represent the passive control forces fed back by the master force feedback device and the slave robot, respectively. and These represent the passive damping coefficient and passive gain coefficient of the master force feedback device or the slave robot, respectively. and These represent the passive damping coefficient and passive gain coefficient of the main force feedback device, respectively. and This represents the passive damping coefficient and passive gain coefficient of the feedback from the end-user robot. Indicates the position of the master force feedback device or the slave robot. and These represent the positions of the master force feedback device and the slave robot, respectively. The derivative representing the position of the master force feedback device or the slave robot. and Let represent the derivatives of the positions of the master force feedback device and the slave robot, respectively; The passive constraint is as follows: ; in, This represents the damping coefficient of the master-end force feedback device or the slave-end robot. and These represent the damping coefficients of the master-end force feedback device and the slave-end robot, respectively. Indicates the equivalent velocity coefficient; This indicates the mass of the master force feedback device or the slave robot. and These represent the mass of the master force feedback device and the slave robot, respectively.

Citation Information

Patent Citations

  • Nonlinear teleoperation bilateral control method based on adaptive fuzzy inversion

    CN109085749A

  • Hexapod robot teleoperation control method applied to variable time delay condition

    CN113721526A